Enter the raw data point, population mean, and standard deviation into the calculator below to determine the z-score, also known as the standard score.

Z-Score Formula

The following formula is used to calculate the z-score:

z score formula
  • Where μ is the mean of the population
  • and σ is the standard deviation of the population
  • x is the raw data point

The Z score can also be determined using a table such as provided below.

Image result for z score confidence level table

Z Score Definition

A z-score, also known as a standard score, is a term used in statistics to describe a signed fractional number of standard deviations by which the value of a data point is above the mean value.

A Z-score is used to compare observational data to theoretical deviation. Determining the z-score requires that one knows the mean and standard deviation of a total population that the data in question belongs to.

Since z-score is used to compare observed data to theoretical data, another way of looking at it is to say that it’s a measure of confidence in a data set. This means that a z-score directly correlates with a confidence interval

How to calculate a z-score?

The following is a step by step guide on how to calculate the z-score:

  1. Through analyzing the formula above, we know the first step will be to acquire the mean of the population.
  2. For this example, we will assume the mean is 20.
  3. The next step is to determine the standard deviation of the population. For this example let’s assume the deviation is 1.5.
  4. Finally, we must measure our raw data value of x. We find that x is 25.
  5. The last step is to plug all of this information into the formula above to get our answer. We find the z-score of this problem to be 3.33

Analyze your results and apply to future problems.


What does a Z-Score indicate?

A Z-Score indicates how many standard deviations an element is from the mean. A positive Z-Score means the data point is above the mean, while a negative Z-Score means it’s below the mean.

Why is the Z-Score important in statistics?

The Z-Score is important because it allows for comparisons between different data sets or within the same data set over time, and it helps identify outliers.

Can Z-Scores be used for all types of data?

Z-Scores are most effective with data that is normally distributed. For data that does not follow a normal distribution, other methods of standardization might be more appropriate.

How does the Z-Score relate to the standard normal distribution?

The Z-Score is a key part of the standard normal distribution. It is used to determine where a data point lies within the distribution, helping to calculate probabilities and confidence intervals.